@Max Balesteri there are many, many questions, I'll try to name a few I would want to know.
1. Ask if they do in-house maintenance or do they contract out all repairs.
2. At what level do they need your approval to conduct repairs (i.e. if something is going to cost over $200.00 do they call you first).
3. What is their process for past due rent - collections - and lease violations.
4. On top of what @Curt Davis said, get a list of all fees they charge - lease up fee - marketing fee - anything you might be charged for, though all this should be in the management agreement.
5. If they have an indemnity clause and how it is written (do you the investor shoulder all of the burden in a legal dispute).
6. When is rent due, when is your distribution sent if the tenant pays on time/and when if the tenant is late? What is the late fee policy and who receives the money from late fees? Is is check or direct deposit?
7. Do they provide online statements or do they mail out a monthly statement?
Some other tips - before deciding get a proposal from 3 different companies make sure they include their fees - along with a copy of their management agreement and lease so you can review and compare them. I am not saying paying higher fees is necessarily bad if it give you peace of mind and the company does a good job, just make sure you don't get any surprises - tenants can be surprising enough.